MODELOS DE BENCHMARK#
import warnings
warnings.filterwarnings("ignore")
import pandas as pd
import numpy as np
import plotly.express as px
import plotly.io as pio
import plotly.express as px
import plotly.offline as py
pio.renderers.default = "notebook"
import seaborn as sns
import matplotlib.dates as mdates
import mplfinance as mpf
from sklearn.model_selection import train_test_split
from statsmodels.tsa.holtwinters import ExponentialSmoothing
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.statespace.sarimax import SARIMAX
from statsmodels.tsa.holtwinters import SimpleExpSmoothing
from sklearn.metrics import mean_absolute_percentage_error, mean_squared_error
import math
from sklearn.model_selection import GridSearchCV
from keras.wrappers.scikit_learn import KerasRegressor
Preparación de datos#
para el modelamiento de la series se escogerá el precio de serie de la acción. También Se asignará la fecha como eje x. Así mismo se hará la división dde los datos entre entrenamiento y prueba
data = pd.read_csv(r"C:\Users\claud\OneDrive - Universidad del Norte\Escritorio\Series de tiempo\Natural_Gas_data.csv")
data['date'] = pd.to_datetime(data['date'])
data.set_index('date', inplace=True)
data_index = data.index
y = data['close'].values
# Primero, dividimos en train + val y test (85% para train + val, 15% para test)
y_train_val, y_test = train_test_split(y, test_size=0.15, shuffle=False)
# Luego, dividimos el train + val en train (70%) y val (30% de ese subconjunto)
y_train, y_val = train_test_split(y_train_val, test_size=0.3, shuffle=False)
# Verificando las formas de los conjuntos
print(f'Tamaño de entrenamiento: {len(y_train)}')
print(f'Tamaño de validación: {len(y_val)}')
print(f'Tamaño de prueba: {len(y_test)}')
Tamaño de entrenamiento: 3558
Tamaño de validación: 1525
Tamaño de prueba: 897
Dividimos los datos en entrenamiento, validación y test
metrics_list = []
Se realizó una función para graficar los modelos
import numpy as np
import pandas as pd
import plotly.express as px
def plot_model_results_plotly(y_train, y_train_pred, y_val, y_val_pred, y_test, y_pred, data_index, train_size, val_size, title):
# Crear un índice completo basado en la longitud total de los datos
data_index_full = data_index[:len(y_train) + len(y_val) + len(y_test)]
# Extender las listas para alinear los datos con el índice completo
y_train_extended = np.concatenate([y_train, [None] * (len(y_val) + len(y_test))])
y_train_pred_full = np.concatenate([y_train_pred, [None] * (len(y_train_extended) - len(y_train_pred))])
y_val_extended = np.concatenate([[None] * len(y_train), y_val, [None] * len(y_test)])
y_val_pred_full = np.concatenate([[None] * len(y_train), y_val_pred, [None] * (len(y_test))])
y_test_extended = np.concatenate([[None] * (len(y_train) + len(y_val)), y_test])
y_pred_full = np.concatenate([[None] * (len(y_train) + len(y_val)), y_pred])
# Crear DataFrame para la gráfica
df_plot = pd.DataFrame({
'Fecha': data_index_full,
'Datos de entrenamiento': y_train_extended,
'Modelo entrenado': y_train_pred_full,
'Datos de validación': y_val_extended,
'Predicción validación': y_val_pred_full,
'Datos de prueba': y_test_extended,
'Predicción prueba': y_pred_full
})
# Graficar con Plotly
fig = px.line(
df_plot, x='Fecha',
y=[
'Datos de entrenamiento', 'Modelo entrenado',
'Datos de validación', 'Predicción validación',
'Datos de prueba', 'Predicción prueba'
],
title=title, labels={'value': 'Valor', 'Fecha': 'Fecha'}
)
fig.show()
función para caluclar metricas y guardarlas en una lista para posteriormente crear la tabla y comparar
def calculate_and_store_metrics(model, model_name, y_train, y_train_pred, y_val, y_val_pred, y_test, y_pred):
# Cálculo de métricas para el conjunto de prueba
mape_test = mean_absolute_percentage_error(y_test, y_pred)
rmse_test = mean_squared_error(y_test, y_pred, squared=False)
# Cálculo de métricas para el conjunto de validación
mape_val = mean_absolute_percentage_error(y_val, y_val_pred)
rmse_val = mean_squared_error(y_val, y_val_pred, squared=False)
# Almacenando las métricas en la lista
metrics_list.append({
'Modelo': model_name,
'MAPE Prueba': mape_test,
'RMSE Prueba': rmse_test,
'MAPE Validación': mape_val,
'RMSE Validación': rmse_val
})
función para comprobar supuestos
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import statsmodels.api as sm
from scipy.stats import shapiro # Corrección: Usamos shapiro desde scipy
def check_model_assumptions(model, y_train, y_train_pred, y_val, y_val_pred, y_test, y_test_pred):
# Calcular los residuales
resid_train = y_train - y_train_pred
resid_val = y_val - y_val_pred
resid_test = y_test - y_test_pred
print("\n----- Pruebas de Hipótesis sobre los Supuestos -----")
# Prueba de Normalidad (Shapiro-Wilk) para entrenamiento
stat, p_value = shapiro(resid_train)
print(f"Shapiro-Wilk p-value (Entrenamiento): {p_value:.4f}")
print("Conclusión:", "NO sigue una distribución normal.\n" if p_value < 0.05 else "Sigue una distribución normal.\n")
# Prueba de Autocorrelación (Ljung-Box) para entrenamiento
lb_test = sm.stats.acorr_ljungbox(resid_train, lags=[10], return_df=True)
lb_p_value = lb_test['lb_pvalue'].values[0]
print(f"Ljung-Box p-value (Entrenamiento): {lb_p_value:.4f}")
print("Conclusión:", "Autocorrelación significativa.\n" if lb_p_value < 0.05 else "Sin autocorrelación significativa.\n")
# Prueba de Homocedasticidad (Breusch-Pagan) para entrenamiento
exog = sm.add_constant(np.arange(len(resid_train)).reshape(-1, 1))
_, bp_p_value, _, _ = sm.stats.het_breuschpagan(resid_train, exog)
print(f"Breusch-Pagan p-value (Entrenamiento): {bp_p_value:.4f}")
print("Conclusión:", "Varianza no constante.\n" if bp_p_value < 0.05 else "Varianza constante.\n")
# Crear figuras en Matplotlib
fig, axes = plt.subplots(2, 3, figsize=(18, 10))
fig.suptitle('Verificación de los Supuestos del Modelo')
# Histograma de los residuales de entrenamiento
axes[0, 0].hist(resid_train, bins=20, edgecolor='black')
axes[0, 0].set_title('Histograma (Entrenamiento)')
axes[0, 0].set_xlabel('Residual')
axes[0, 0].set_ylabel('Frecuencia')
# Q-Q Plot de los residuales de entrenamiento
sm.qqplot(resid_train, line='s', ax=axes[0, 1])
axes[0, 1].set_title('Q-Q Plot (Entrenamiento)')
# ACF de los residuales de entrenamiento
sm.graphics.tsa.plot_acf(resid_train, ax=axes[0, 2], lags=30)
axes[0, 2].set_title('ACF (Entrenamiento)')
# Histograma de los residuales de validación
axes[1, 0].hist(resid_val, bins=20, edgecolor='black')
axes[1, 0].set_title('Histograma (Validación)')
axes[1, 0].set_xlabel('Residual')
axes[1, 0].set_ylabel('Frecuencia')
# Q-Q Plot de los residuales de validación
sm.qqplot(resid_val, line='s', ax=axes[1, 1])
axes[1, 1].set_title('Q-Q Plot (Validación)')
# ACF de los residuales de validación
sm.graphics.tsa.plot_acf(resid_val, ax=axes[1, 2], lags=30)
axes[1, 2].set_title('ACF (Validación)')
plt.tight_layout(rect=[0, 0, 1, 0.96]) # Ajustar layout para evitar superposición
plt.show()
Suavización exponencial#
Función para optimizar y encontrar el mejor modelo de suavización exponencial para compararlos se uso la metrica AIC ya que esta penaliza el sobre ajuste. Se preuban las posibles combianciones de suavización exponencial
import numpy as np
from statsmodels.tsa.holtwinters import ExponentialSmoothing
def optimize_exponential_smoothing(y_train, y_val, y_test, model_name, trend=None, seasonal=None, seasonal_periods=None):
"""Optimiza un modelo de suavización exponencial."""
best_aic = float('inf')
best_params = None
best_model = None
# Rango de valores para los parámetros
smoothing_level_values = np.linspace(0.1, 1.0, 10)
smoothing_slope_values = np.linspace(0.1, 1.0, 10)
smoothing_seasonal_values = np.linspace(0.1, 1.0, 10)
seasonal_periods_values = [2, 3, 4, 6, 12]
# Búsqueda de los mejores parámetros
for alpha in smoothing_level_values:
for beta in smoothing_slope_values:
if seasonal:
for gamma in smoothing_seasonal_values:
for period in seasonal_periods_values:
try:
model = ExponentialSmoothing(y_train, trend=trend, seasonal=seasonal,
seasonal_periods=period).fit(
smoothing_level=alpha, smoothing_slope=beta,
smoothing_seasonal=gamma, optimized=False)
aic = model.aic
if aic < best_aic:
best_aic, best_params, best_model = aic, (alpha, beta, gamma, period), model
except Exception as e:
print(f"Error: {e}")
continue
else:
try:
model = ExponentialSmoothing(y_train, trend=trend).fit(
smoothing_level=alpha, smoothing_slope=beta, optimized=False)
aic = model.aic
if aic < best_aic:
best_aic, best_params, best_model = aic, (alpha, beta), model
except Exception as e:
print(f"Error: {e}")
continue
return best_aic, best_params, best_model
def evaluate_all_models(y_train, y_val, y_test):
"""Evalúa los tres tipos de suavización y selecciona el mejor modelo."""
results = []
# Evaluar Suavización Simple
aic_simple, params_simple, model_simple = optimize_exponential_smoothing(
y_train, y_val, y_test, 'Suavización Exponencial Simple')
# Evaluar Suavización Doble
aic_double, params_double, model_double = optimize_exponential_smoothing(
y_train, y_val, y_test, 'Suavización Exponencial Doble', trend='add')
# Evaluar Suavización Triple
aic_triple, params_triple, model_triple = optimize_exponential_smoothing(
y_train, y_val, y_test, 'Suavización Exponencial Triple', trend='add', seasonal='add', seasonal_periods=12)
# Guardar resultados
results.append(('Simple', aic_simple, model_simple))
results.append(('Doble', aic_double, model_double))
results.append(('Triple', aic_triple, model_triple))
# Seleccionar el mejor modelo según el AIC más bajo
best_model_name, best_aic, best_model = min(results, key=lambda x: x[1])
print(f"El mejor modelo es: {best_model_name} con AIC={best_aic}")
# Predicciones del mejor modelo
y_train_pred = best_model.fittedvalues
y_val_pred = best_model.forecast(steps=len(y_val))
y_pred = best_model.forecast(steps=len(y_test) + len(y_val))[-len(y_test):]
# Calcular métricas y generar gráficas solo para el mejor modelo
calculate_and_store_metrics(best_model, best_model_name, y_train, y_train_pred, y_val, y_val_pred, y_test, y_pred)
plot_model_results_plotly(y_train, y_train_pred, y_val, y_val_pred, y_test, y_pred,
data.index, len(y_train), len(y_val), best_model_name)
check_model_assumptions(best_model, y_train, y_train_pred, y_val, y_val_pred, y_test, y_pred)
# Ejemplo de uso
evaluate_all_models(y_train, y_val, y_test)
El mejor modelo es: Simple con AIC=-11007.7581873107
----- Pruebas de Hipótesis sobre los Supuestos -----
Shapiro-Wilk p-value (Entrenamiento): 0.0000
Conclusión: NO sigue una distribución normal.
Ljung-Box p-value (Entrenamiento): 0.0053
Conclusión: Autocorrelación significativa.
Breusch-Pagan p-value (Entrenamiento): 0.0000
Conclusión: Varianza no constante.
Los supuestos no se cumplieron este modelo no es valido. los residuales no son normales. no son independientes y no son aleatorios. esto se debe a que estos modelos no alcanzan a interpretar la complejidad de la serie por lo que no daran buenos resultados
Modelos Autoregresivos#
Al igual que con suavización exponencial se hizo una comparación entre los posibles parametros de los modelos autoregresivos para encontrar el mejor modelo comparnado la metrica AIC
# Librerías comunes para todos los modelos
import numpy as np
import pandas as pd
import plotly.graph_objects as go
from sklearn.metrics import mean_squared_error, mean_absolute_percentage_error
from sklearn.model_selection import GridSearchCV
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU, Conv1D, MaxPooling1D, Flatten
from sklearn.neural_network import MLPRegressor
import plotly.io as pio
import plotly.express as px
import plotly.offline as py
pio.renderers.default = "notebook"
import warnings
warnings.filterwarnings("ignore")
Implementamos el mismo modelo ARIMA al cual posteriormente le tartaremos los residuales para mejorar los resultados del modelo
import numpy as np
import pandas as pd
from statsmodels.tsa.arima.model import ARIMA
# Definir rangos de búsqueda para p, d y q
p_values = range(0, 3)
d_values = range(0, 2)
q_values = range(0, 6)
def rolling_forecast(order, y_train, y_val, y_test):
history = list(y_train) # Usar datos de entrenamiento como historial inicial
val_predictions = []
test_predictions = []
# Predecir para el conjunto de validación
for t in range(len(y_val)):
model = ARIMA(history, order=order).fit()
yhat = model.forecast()[0]
val_predictions.append(yhat)
history.append(y_val[t]) # Actualizar el historial con el dato real
# Predecir para el conjunto de prueba
for t in range(len(y_test)):
model = ARIMA(history, order=order).fit()
yhat = model.forecast()[0]
test_predictions.append(yhat)
history.append(y_test[t]) # Actualizar el historial con el dato real
return np.array(val_predictions), np.array(test_predictions)
def optimize_model(order_range, y_train):
"""Optimiza el modelo ARIMA para los parámetros dados."""
best_aic = float("inf")
best_params = None
best_model = None
for p in order_range[0]:
for d in order_range[1]:
for q in order_range[2]:
try:
model = ARIMA(y_train, order=(p, d, q)).fit()
aic = model.aic
if aic < best_aic:
best_aic = aic
best_params = (p, d, q)
best_model = model
except Exception as e:
print(f"Error: {e}")
continue
print(f"Mejores parámetros: p={best_params[0]}, d={best_params[1]}, q={best_params[2]} con AIC={best_aic}")
return best_model, best_params
def evaluate_models(y_train, y_val, y_test, data):
"""Evalúa todos los modelos y selecciona el mejor."""
models = [
('AR', (p_values, [0], [0])),
('MA', ([0], [0], q_values)),
('ARIMA', (p_values, d_values, q_values))
]
best_aic = float("inf")
best_model_name = None
best_model = None
best_params = None
for model_name, order_range in models:
print(f"Evaluando: {model_name}")
model, params = optimize_model(order_range, y_train)
if model.aic < best_aic:
best_aic = model.aic
best_model_name = model_name
best_model = model
best_params = params
print(f"\nEl mejor modelo es: {best_model_name} con AIC={best_aic}")
# Rolling forecast para validación y prueba
y_val_pred, y_test_pred = rolling_forecast(best_params, y_train, y_val, y_test)
y_train_pred = best_model.fittedvalues
# Calcular y almacenar métricas
calculate_and_store_metrics(best_model, best_model_name, y_train, y_train_pred, y_val, y_val_pred, y_test, y_test_pred)
# Graficar los resultados
plot_model_results_plotly(y_train, y_train_pred, y_val, y_val_pred, y_test, y_test_pred, data.index, len(y_train), len(y_val), best_model_name)
# Verificar supuestos del mejor modelo
check_model_assumptions(best_model, y_train, y_train_pred, y_val, y_val_pred, y_test, y_test_pred)
evaluate_models(y_train, y_val, y_test, data)
Evaluando: AR
Mejores parámetros: p=1, d=0, q=0 con AIC=-911.4617908954825
Evaluando: MA
Mejores parámetros: p=0, d=0, q=5 con AIC=3438.3500291627465
Evaluando: ARIMA
Mejores parámetros: p=2, d=1, q=5 con AIC=-923.2849978518195
El mejor modelo es: ARIMA con AIC=-923.2849978518195
----- Pruebas de Hipótesis sobre los Supuestos -----
Shapiro-Wilk p-value (Entrenamiento): 0.0000
Conclusión: NO sigue una distribución normal.
Ljung-Box p-value (Entrenamiento): 0.9600
Conclusión: Sin autocorrelación significativa.
Breusch-Pagan p-value (Entrenamiento): 0.0000
Conclusión: Varianza no constante.
El modelo arima tuvo emjores resultados sin embargo, no cumple los supuestos,no distribuye normal, no tiene varianza constante y los residuos no son independientes. este modelo no es válido para hacer conclusiones
RNN#
Se utlizó una grid search para encontrar los mejores parametros
import numpy as np
import pandas as pd
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import SimpleRNN, Dense, Dropout
from sklearn.model_selection import train_test_split, GridSearchCV
from sklearn.metrics import mean_squared_error
import matplotlib.pyplot as plt
# Dividir los datos en entrenamiento, validación y prueba
y_train_val, y_test = train_test_split(y, test_size=0.15, shuffle=False)
y_train, y_val = train_test_split(y_train_val, test_size=0.3, shuffle=False)
print(f'Tamaño de entrenamiento: {len(y_train)}')
print(f'Tamaño de validación: {len(y_val)}')
print(f'Tamaño de prueba: {len(y_test)}')
Tamaño de entrenamiento: 3558
Tamaño de validación: 1525
Tamaño de prueba: 897
# Función para crear el modelo RNN con hiperparámetros variables
def create_rnn(dropout_rate=0.2, neurons=10, n_layers=1):
model = Sequential()
# Añadir capas según el hiperparámetro n_layers
for _ in range(n_layers):
model.add(SimpleRNN(neurons, activation='tanh', return_sequences=True if n_layers > 1 else False,
input_shape=(1, 1)))
model.add(Dropout(dropout_rate))
model.add(Dense(1)) # Capa de salida
model.compile(optimizer='adam', loss='mse')
return model
# Grid Search con KerasRegressor
from tensorflow.keras.wrappers.scikit_learn import KerasRegressor
model = KerasRegressor(build_fn=create_rnn, epochs=10, verbose=0)
# Parámetros para Grid Search extendido
param_grid = {
'batch_size': [16, 32 ],
'dropout_rate': [0.6, 0.8],
'neurons': [50,100],
'n_layers': [1], # Agregamos opción para una o dos capas
'epochs': [10,20]
}
grid_result=0
history=0
# Configuración del GridSearch
grid = GridSearchCV(estimator=model, param_grid=param_grid, cv=3)
grid_result = grid.fit(y_train.reshape(-1, 1, 1), y_train)
# Mostrar los mejores parámetros
print(f'Mejor resultado: {grid_result.best_score_} con parámetros {grid_result.best_params_}')
# Crear y entrenar el mejor modelo
best_params = grid_result.best_params_
final_model = create_rnn(dropout_rate=best_params['dropout_rate'],
neurons=best_params['neurons'],
n_layers=best_params['n_layers'])
history = final_model.fit(y_train.reshape(-1, 1, 1), y_train,
validation_data=(y_val.reshape(-1, 1, 1), y_val),
epochs=50, batch_size=best_params['batch_size'], verbose=1)
# Predicciones
y_train_pred_RNN = final_model.predict(y_train.reshape(-1, 1, 1))
y_val_pred_RNN = final_model.predict(y_val.reshape(-1, 1, 1))
y_test_pred_RNN = final_model.predict(y_test.reshape(-1, 1, 1))
Mejor resultado: -0.040075693589945637 con parámetros {'batch_size': 16, 'dropout_rate': 0.6, 'n_layers': 1, 'neurons': 200}
Epoch 1/50
223/223 [==============================] - 2s 5ms/step - loss: 2.8718 - val_loss: 0.0521
Epoch 2/50
223/223 [==============================] - 1s 4ms/step - loss: 0.7191 - val_loss: 0.0297
Epoch 3/50
223/223 [==============================] - 1s 4ms/step - loss: 0.4926 - val_loss: 0.1125
Epoch 4/50
223/223 [==============================] - 1s 4ms/step - loss: 0.3737 - val_loss: 0.0608
Epoch 5/50
223/223 [==============================] - 1s 4ms/step - loss: 0.3559 - val_loss: 0.0417
Epoch 6/50
223/223 [==============================] - 1s 4ms/step - loss: 0.3260 - val_loss: 0.0390
Epoch 7/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2942 - val_loss: 0.0406
Epoch 8/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2713 - val_loss: 0.0291
Epoch 9/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2944 - val_loss: 0.0639
Epoch 10/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2974 - val_loss: 0.0235
Epoch 11/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2643 - val_loss: 0.0176
Epoch 12/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2826 - val_loss: 0.0366
Epoch 13/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2673 - val_loss: 0.0176
Epoch 14/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2740 - val_loss: 0.0285
Epoch 15/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2439 - val_loss: 0.0130
Epoch 16/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2455 - val_loss: 0.0233
Epoch 17/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2482 - val_loss: 0.0087
Epoch 18/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2572 - val_loss: 0.0091
Epoch 19/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2405 - val_loss: 0.0197
Epoch 20/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2219 - val_loss: 0.0032
Epoch 21/50
223/223 [==============================] - 1s 3ms/step - loss: 0.2535 - val_loss: 0.0106
Epoch 22/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2344 - val_loss: 0.0164
Epoch 23/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2296 - val_loss: 0.0036
Epoch 24/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2324 - val_loss: 0.0161
Epoch 25/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2117 - val_loss: 0.0194
Epoch 26/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2182 - val_loss: 0.0146
Epoch 27/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2045 - val_loss: 0.0085
Epoch 28/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2248 - val_loss: 0.0027
Epoch 29/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2075 - val_loss: 0.0081
Epoch 30/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2023 - val_loss: 0.0029
Epoch 31/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2055 - val_loss: 0.0176
Epoch 32/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1937 - val_loss: 0.0349
Epoch 33/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1969 - val_loss: 0.0020
Epoch 34/50
223/223 [==============================] - 1s 4ms/step - loss: 0.2084 - val_loss: 0.0136
Epoch 35/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1885 - val_loss: 0.0091
Epoch 36/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1740 - val_loss: 0.0044
Epoch 37/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1795 - val_loss: 0.0501
Epoch 38/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1933 - val_loss: 0.0090
Epoch 39/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1722 - val_loss: 0.0195
Epoch 40/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1785 - val_loss: 0.0140
Epoch 41/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1734 - val_loss: 0.0089
Epoch 42/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1781 - val_loss: 7.1334e-04
Epoch 43/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1589 - val_loss: 0.0012
Epoch 44/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1654 - val_loss: 0.0118
Epoch 45/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1578 - val_loss: 0.0044
Epoch 46/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1473 - val_loss: 0.0190
Epoch 47/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1452 - val_loss: 0.0058
Epoch 48/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1546 - val_loss: 0.0070
Epoch 49/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1510 - val_loss: 0.0321
Epoch 50/50
223/223 [==============================] - 1s 4ms/step - loss: 0.1421 - val_loss: 0.0017
112/112 [==============================] - 0s 2ms/step
48/48 [==============================] - 0s 4ms/step
29/29 [==============================] - 0s 2ms/step
calculate_and_store_metrics(
model=final_model,
model_name='RNN Mejor Modelo',
y_train=y_train, y_train_pred =y_train_pred_RNN,
y_val=y_val, y_val_pred=y_val_pred_RNN,
y_test=y_test, y_pred =y_test_pred_RNN
)
plot_model_results_plotly(y_train=y_train,
y_train_pred=y_train_pred_RNN .reshape(-1),
y_val=y_val,
y_val_pred=y_val_pred_RNN .reshape(-1),
y_test=y_test,
y_pred=y_test_pred_RNN .reshape(-1),
data_index=data.index, train_size= len(y_train),
val_size=len(y_val),title= 'RNN - Predicción del Precio de Cierre')
check_model_assumptions(
model=final_model,
y_train=y_train .reshape(-1), y_train_pred=y_train_pred_RNN .reshape(-1),
y_val=y_val, y_val_pred=y_val_pred_RNN.reshape(-1),
y_test=y_test, y_test_pred=y_test_pred_RNN
)
----- Pruebas de Hipótesis sobre los Supuestos -----
Shapiro-Wilk p-value (Entrenamiento): 0.0000
Conclusión: NO sigue una distribución normal.
Ljung-Box p-value (Entrenamiento): 0.0000
Conclusión: Autocorrelación significativa.
Breusch-Pagan p-value (Entrenamiento): 0.0000
Conclusión: Varianza no constante.
{‘batch_size’: 16, ‘dropout_rate’: 0.6, ‘epochs’: 20, ‘n_layers’: 1, ‘neurons’: 100} estos fueron los mejores parametros y aunque el error no es pronunciado los resiudos no cumplen con ninguno de los supuestos.
LSTM#
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import LSTM, Dense, Dropout
from sklearn.model_selection import train_test_split, GridSearchCV
from tensorflow.keras.wrappers.scikit_learn import KerasRegressor
from math import sqrt
# Función para crear el modelo LSTM con hiperparámetros variables
def create_lstm(dropout_rate=0.3, neurons=10, n_layers=1):
model = Sequential()
for _ in range(n_layers):
model.add(LSTM(neurons, activation='relu',
return_sequences=True if n_layers > 1 else False,
input_shape=(1, 1)))
model.add(Dropout(dropout_rate))
model.add(Dense(1)) # Capa de salida para regresión
model.compile(optimizer='adam', loss='mse')
return model
# Configurar el modelo con KerasRegressor para GridSearch
model = KerasRegressor(build_fn=create_lstm, epochs=10, verbose=0)
grid_result=0
history=0
# Parámetros para Grid Search extendido
param_grid = {
'batch_size': [16, 64],
'dropout_rate': [0.3, 0.6],
'neurons': [20, 40],
'n_layers': [1, 2] # Opción para 1 o 2 capas
}
# Grid Search con validación cruzada
grid = GridSearchCV(estimator=model, param_grid=param_grid, cv=3)
grid_result = grid.fit(y_train.reshape(-1, 1, 1), y_train)
# Mostrar los mejores parámetros
print(f'Mejor resultado: {grid_result.best_score_} con parámetros {grid_result.best_params_}')
# Crear y entrenar el mejor modelo
best_params = grid_result.best_params_
final_model = create_lstm(
dropout_rate=best_params['dropout_rate'],
neurons=best_params['neurons'],
n_layers=best_params['n_layers']
)
history = final_model.fit(
y_train.reshape(-1, 1, 1), y_train,
validation_data=(y_val.reshape(-1, 1, 1), y_val),
epochs=50, batch_size=best_params['batch_size'], verbose=1
)
# Predicciones
y_train_pred_lstm= final_model.predict(y_train.reshape(-1, 1, 1))
y_val_pred_lstm = final_model.predict(y_val.reshape(-1, 1, 1))
y_test_pred_lstm = final_model.predict(y_test.reshape(-1, 1, 1))
Mejor resultado: -0.0235072560608387 con parámetros {'batch_size': 16, 'dropout_rate': 0.3, 'n_layers': 1, 'neurons': 40}
Epoch 1/50
223/223 [==============================] - 1s 3ms/step - loss: 9.5585 - val_loss: 0.3830
Epoch 2/50
223/223 [==============================] - 0s 2ms/step - loss: 1.4181 - val_loss: 0.1853
Epoch 3/50
223/223 [==============================] - 1s 3ms/step - loss: 1.2165 - val_loss: 0.0733
Epoch 4/50
223/223 [==============================] - 0s 2ms/step - loss: 0.9888 - val_loss: 0.0221
Epoch 5/50
223/223 [==============================] - 0s 2ms/step - loss: 0.9676 - val_loss: 0.0074
Epoch 6/50
223/223 [==============================] - 1s 2ms/step - loss: 0.9201 - val_loss: 0.0093
Epoch 7/50
223/223 [==============================] - 0s 2ms/step - loss: 0.8329 - val_loss: 0.0130
Epoch 8/50
223/223 [==============================] - 1s 2ms/step - loss: 0.8388 - val_loss: 0.0120
Epoch 9/50
223/223 [==============================] - 1s 3ms/step - loss: 0.8491 - val_loss: 0.0167
Epoch 10/50
223/223 [==============================] - 1s 2ms/step - loss: 0.8159 - val_loss: 0.0292
Epoch 11/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7853 - val_loss: 0.0203
Epoch 12/50
223/223 [==============================] - 1s 2ms/step - loss: 0.7828 - val_loss: 0.0265
Epoch 13/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7792 - val_loss: 0.0291
Epoch 14/50
223/223 [==============================] - 1s 2ms/step - loss: 0.7733 - val_loss: 0.0336
Epoch 15/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7143 - val_loss: 0.0338
Epoch 16/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7297 - val_loss: 0.0398
Epoch 17/50
223/223 [==============================] - 1s 2ms/step - loss: 0.7140 - val_loss: 0.0646
Epoch 18/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6889 - val_loss: 0.0737
Epoch 19/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6153 - val_loss: 0.0602
Epoch 20/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6646 - val_loss: 0.0620
Epoch 21/50
223/223 [==============================] - 1s 2ms/step - loss: 0.6367 - val_loss: 0.0858
Epoch 22/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6416 - val_loss: 0.0755
Epoch 23/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6309 - val_loss: 0.1023
Epoch 24/50
223/223 [==============================] - 1s 2ms/step - loss: 0.5959 - val_loss: 0.1099
Epoch 25/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6026 - val_loss: 0.1272
Epoch 26/50
223/223 [==============================] - 1s 2ms/step - loss: 0.6015 - val_loss: 0.1353
Epoch 27/50
223/223 [==============================] - 1s 2ms/step - loss: 0.5487 - val_loss: 0.1298
Epoch 28/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5639 - val_loss: 0.1853
Epoch 29/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5181 - val_loss: 0.1481
Epoch 30/50
223/223 [==============================] - 1s 2ms/step - loss: 0.5394 - val_loss: 0.1371
Epoch 31/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5604 - val_loss: 0.1794
Epoch 32/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5115 - val_loss: 0.1836
Epoch 33/50
223/223 [==============================] - 1s 2ms/step - loss: 0.5065 - val_loss: 0.1734
Epoch 34/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5092 - val_loss: 0.2081
Epoch 35/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5008 - val_loss: 0.1592
Epoch 36/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4792 - val_loss: 0.2197
Epoch 37/50
223/223 [==============================] - 1s 2ms/step - loss: 0.4761 - val_loss: 0.2147
Epoch 38/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4461 - val_loss: 0.2195
Epoch 39/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4586 - val_loss: 0.2065
Epoch 40/50
223/223 [==============================] - 1s 2ms/step - loss: 0.4514 - val_loss: 0.2273
Epoch 41/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4362 - val_loss: 0.1865
Epoch 42/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4433 - val_loss: 0.2541
Epoch 43/50
223/223 [==============================] - 1s 2ms/step - loss: 0.4339 - val_loss: 0.2361
Epoch 44/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4049 - val_loss: 0.2280
Epoch 45/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3962 - val_loss: 0.2427
Epoch 46/50
223/223 [==============================] - 1s 2ms/step - loss: 0.3634 - val_loss: 0.2258
Epoch 47/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3665 - val_loss: 0.2330
Epoch 48/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3660 - val_loss: 0.2567
Epoch 49/50
223/223 [==============================] - 1s 2ms/step - loss: 0.3783 - val_loss: 0.2590
Epoch 50/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3663 - val_loss: 0.2836
112/112 [==============================] - 0s 1ms/step
48/48 [==============================] - 0s 3ms/step
29/29 [==============================] - 0s 1ms/step
calculate_and_store_metrics(
model=final_model,
model_name='LSTM',
y_train=y_train,
y_train_pred=y_train_pred_lstm,
y_val=y_val,
y_val_pred=y_val_pred_lstm,
y_test=y_test,
y_pred=y_test_pred_lstm
)
# Llamada a la función para graficar
plot_model_results_plotly(
y_train=y_train,
y_train_pred=y_train_pred_lstm.reshape(-1),
y_val=y_val,
y_val_pred=y_val_pred_lstm.reshape(-1),
y_test=y_test,
y_pred=y_test_pred_lstm.reshape(-1),
data_index=data.index,
train_size=len(y_train),
val_size=len(y_val),
title='LSTM - Predicción del Precio de Cierre'
)
check_model_assumptions(
model=final_model,
y_train=y_train.reshape(-1), y_train_pred=y_train_pred_lstm.reshape(-1),
y_val=y_val, y_val_pred=y_val_pred_lstm.reshape(-1),
y_test=y_test, y_test_pred=y_test_pred_lstm
)
----- Pruebas de Hipótesis sobre los Supuestos -----
Shapiro-Wilk p-value (Entrenamiento): 0.0000
Conclusión: NO sigue una distribución normal.
Ljung-Box p-value (Entrenamiento): 0.0000
Conclusión: Autocorrelación significativa.
Breusch-Pagan p-value (Entrenamiento): 0.0099
Conclusión: Varianza no constante.
EL modelo no cumple
Redes Neuronales modelo MLp#
# Función para crear el modelo MLP con hiperparámetros variables
def create_mlp(dropout_rate=0.8, neurons=10, n_layers=1):
model = Sequential()
for _ in range(n_layers):
model.add(Dense(neurons, activation='relu', input_shape=(1,)))
model.add(Dropout(dropout_rate))
model.add(Dense(1)) # Capa de salida para regresión
model.compile(optimizer='adam', loss='mse')
return model
history=[]
grid=None
grid_result=0
best_params=0
model=0
# Configuración del modelo con KerasRegressor para GridSearch
model = KerasRegressor(build_fn=create_mlp, epochs=10, verbose=0)
# Parámetros para Grid Search extendido
param_grid = {
'batch_size': [16, 64],
'dropout_rate': [0.6, 0.8],
'neurons': [100,200],
'n_layers': [1]
}
# Grid Search con validación cruzada
grid = GridSearchCV(estimator=model, param_grid=param_grid, cv=3)
grid_result = grid.fit(y_train.reshape(-1, 1), y_train)
# Mostrar los mejores parámetros
print(f'Mejor resultado: {grid_result.best_score_} con parámetros {grid_result.best_params_}')
# Crear y entrenar el mejor modelo
best_params = grid_result.best_params_
final_model = create_mlp(
dropout_rate=best_params['dropout_rate'],
neurons=best_params['neurons'],
n_layers=best_params['n_layers']
)
history = final_model.fit(
y_train.reshape(-1, 1), y_train,
validation_data=(y_val.reshape(-1, 1), y_val),
epochs=50, batch_size=best_params['batch_size'], verbose=1
)
# Predicciones
y_train_pred_mlp = final_model.predict(y_train.reshape(-1, 1))
y_val_pred_mlp = final_model.predict(y_val.reshape(-1, 1))
y_test_pred_mlp = final_model.predict(y_test.reshape(-1, 1))
Mejor resultado: -0.005639246199280024 con parámetros {'batch_size': 16, 'dropout_rate': 0.6, 'n_layers': 1, 'neurons': 200}
Epoch 1/50
223/223 [==============================] - 1s 4ms/step - loss: 3.0600 - val_loss: 0.0168
Epoch 2/50
223/223 [==============================] - 0s 2ms/step - loss: 1.0338 - val_loss: 0.0024
Epoch 3/50
223/223 [==============================] - 0s 2ms/step - loss: 0.9176 - val_loss: 0.0061
Epoch 4/50
223/223 [==============================] - 0s 2ms/step - loss: 0.8072 - val_loss: 0.0029
Epoch 5/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7688 - val_loss: 3.5412e-04
Epoch 6/50
223/223 [==============================] - 0s 2ms/step - loss: 0.7143 - val_loss: 0.0032
Epoch 7/50
223/223 [==============================] - 0s 1ms/step - loss: 0.6643 - val_loss: 0.0020
Epoch 8/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6495 - val_loss: 9.2519e-04
Epoch 9/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6393 - val_loss: 8.0869e-04
Epoch 10/50
223/223 [==============================] - 0s 2ms/step - loss: 0.6377 - val_loss: 4.1723e-04
Epoch 11/50
223/223 [==============================] - 1s 3ms/step - loss: 0.6383 - val_loss: 4.5133e-04
Epoch 12/50
223/223 [==============================] - 1s 4ms/step - loss: 0.6037 - val_loss: 0.0017
Epoch 13/50
223/223 [==============================] - 1s 3ms/step - loss: 0.6057 - val_loss: 0.0010
Epoch 14/50
223/223 [==============================] - 1s 4ms/step - loss: 0.5765 - val_loss: 0.0054
Epoch 15/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5572 - val_loss: 4.8373e-04
Epoch 16/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5345 - val_loss: 5.1362e-04
Epoch 17/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5136 - val_loss: 5.9116e-04
Epoch 18/50
223/223 [==============================] - 1s 2ms/step - loss: 0.5596 - val_loss: 0.0035
Epoch 19/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4799 - val_loss: 0.0018
Epoch 20/50
223/223 [==============================] - 0s 2ms/step - loss: 0.5350 - val_loss: 0.0142
Epoch 21/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4815 - val_loss: 0.0020
Epoch 22/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4585 - val_loss: 7.2793e-04
Epoch 23/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4707 - val_loss: 6.9976e-04
Epoch 24/50
223/223 [==============================] - 0s 1ms/step - loss: 0.4575 - val_loss: 0.0012
Epoch 25/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4512 - val_loss: 0.0010
Epoch 26/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4150 - val_loss: 0.0015
Epoch 27/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4023 - val_loss: 0.0036
Epoch 28/50
223/223 [==============================] - 0s 2ms/step - loss: 0.4136 - val_loss: 0.0069
Epoch 29/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3763 - val_loss: 0.0065
Epoch 30/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3592 - val_loss: 0.0120
Epoch 31/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3757 - val_loss: 0.0099
Epoch 32/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3746 - val_loss: 0.0161
Epoch 33/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3507 - val_loss: 0.0250
Epoch 34/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3242 - val_loss: 0.0342
Epoch 35/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3081 - val_loss: 0.0384
Epoch 36/50
223/223 [==============================] - 0s 2ms/step - loss: 0.3482 - val_loss: 0.0463
Epoch 37/50
223/223 [==============================] - 0s 2ms/step - loss: 0.2772 - val_loss: 0.0598
Epoch 38/50
223/223 [==============================] - 0s 1ms/step - loss: 0.3009 - val_loss: 0.0783
Epoch 39/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2939 - val_loss: 0.0946
Epoch 40/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2896 - val_loss: 0.1060
Epoch 41/50
223/223 [==============================] - 0s 2ms/step - loss: 0.2611 - val_loss: 0.1229
Epoch 42/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2697 - val_loss: 0.1376
Epoch 43/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2813 - val_loss: 0.1608
Epoch 44/50
223/223 [==============================] - 0s 2ms/step - loss: 0.2749 - val_loss: 0.1842
Epoch 45/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2468 - val_loss: 0.1952
Epoch 46/50
223/223 [==============================] - 0s 2ms/step - loss: 0.2390 - val_loss: 0.2156
Epoch 47/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2700 - val_loss: 0.2351
Epoch 48/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2693 - val_loss: 0.2563
Epoch 49/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2698 - val_loss: 0.2618
Epoch 50/50
223/223 [==============================] - 0s 1ms/step - loss: 0.2764 - val_loss: 0.2800
112/112 [==============================] - 0s 694us/step
48/48 [==============================] - 0s 978us/step
29/29 [==============================] - 0s 1ms/step
calculate_and_store_metrics(
model=final_model,
model_name='MLP Mejor Modelo',
y_train=y_train, y_train_pred=y_train_pred_mlp,
y_val=y_val, y_val_pred=y_val_pred_mlp,
y_test=y_test, y_pred=y_test_pred_mlp
)
plot_model_results_plotly(
y_train=y_train,
y_train_pred=y_train_pred_mlp.reshape(-1),
y_val=y_val,
y_val_pred=y_val_pred_mlp.reshape(-1),
y_test=y_test,
y_pred=y_test_pred_mlp.reshape(-1),
data_index=data.index,
train_size=len(y_train),
val_size=len(y_val),
title='MLP - Predicción del Precio de Cierre'
)
# Verificar los residuales con la función proporcionada
check_model_assumptions(
model=final_model,
y_train=y_train.reshape(-1), y_train_pred=y_train_pred_mlp.reshape(-1),
y_val=y_val, y_val_pred=y_val_pred_mlp.reshape(-1),
y_test=y_test, y_test_pred=y_test_pred_mlp
)
----- Pruebas de Hipótesis sobre los Supuestos -----
Shapiro-Wilk p-value (Entrenamiento): 0.0000
Conclusión: NO sigue una distribución normal.
Ljung-Box p-value (Entrenamiento): 0.0000
Conclusión: Autocorrelación significativa.
Breusch-Pagan p-value (Entrenamiento): 0.0000
Conclusión: Varianza no constante.
El modelo no cumple con ninguno de los supuesto por lo que no es un modelo apto.
tabla = pd.DataFrame(metrics_list)
tabla
| Modelo | MAPE Prueba | RMSE Prueba | MAPE Validación | RMSE Validación | |
|---|---|---|---|---|---|
| 0 | Simple | 0.485024 | 1.974356 | 0.606790 | 1.542241 |
| 1 | ARIMA | 0.035799 | 0.238105 | 0.022694 | 0.089031 |
| 2 | RNN Mejor Modelo | 0.026424 | 0.081393 | 0.040286 | 0.101594 |
| 3 | LSTM | 0.171961 | 0.558127 | 0.251937 | 0.670283 |
| 4 | MLP Mejor Modelo | 0.107638 | 0.396454 | 0.164215 | 0.503184 |